Mean shifts, unit roots and forecasting seasonal time series

Examples of descriptive models for changing seasonal patterns in economic time series are autoregressive models with seasonal unit roots or with deterministic seasonal mean shifts. In this paper we show through a forecasting comparison for three macroeconomic time series (for which tests indicate the presence of seasonal unit roots) that allowing for possible seasonal mean shifts can improve forecast performance. Next, by means of simulation we demonstrate the impact of imposing an incorrect model on forecasting. We find that an appropriate decision can deteriorate forecasting performance dramatically in both directions, and hence we recommend the practitioner to take account of seasonal mean shifts when testing for seasonal unit roots.